Antonio Campos scored two goals for Atalante against Juventus on Saturday as the Nerazzurri earned their first points of the season.
The Italian side were looking for their first win in Serie A when they were down to 10 men after 45 minutes.
Ancelotti then put the hosts ahead after 34 minutes with a brilliant finish.
Campos headed home a lovely pass from Marquinhos before slotting home a powerful strike from close range.
Atalanta had to defend to keep the score level, but that proved to be the end of the hosts’ hopes.
Campoes and Atalantico came close to equalising in the second half when Gioinzi Zaffalini had a shot blocked, but the Nerazurri won their way when Dario Pessina sent in a long-range shot from 25 yards.
The result puts Atalanti back on track to defend their European crown after three consecutive losses.